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Calculus · Derivatives

Differentiate 4·pi·r^3/3

\frac{d}{dr}\left[\frac{4 \pi r^{3}}{3}\right]

Step by step

  1. \frac{d}{dr}\left[\frac{4 \pi r^{3}}{3}\right]

    Start from the derivative to compute.

  2. \frac{4 \pi \frac{d}{d r} r^{3}}{3}

    Constant multiple rule: pull the constant out.

  3. 4 \pi r^{2}

    Power rule: (xⁿ)′ = n·xⁿ⁻¹ with n = 3.

Reveal the answer
f'(r) = 4 \pi r^{2}